Jenny,
How should I be deleting the pictures?
if your Library is a managed one, then your delete-workflow is perfect. If it is not managed, then the procedure is a little more complicated.
Managed means, all master files of your images are stored inside your Aperture Library, referenced means they are stored somewhere outside the library. To create a referenced library you either decide at the time of the import to keep your master image files in their current location or to copy/move them into to library. Or you relocate managed master files to a new place outside Aperture.
Since do not know if your masters are referenced or managed, they are probably managed, but you can check that with the badge-overlay:
Referenced images should be displayed in the Browser with a curved arrow in the lower right corner, as described in this article: Understanding Badge Overlays:
We need to know if there are referenced images, because when you delete the images it could be done in a way that the masters will not be deleted along with your version, also you will need storage outside your library.
Regards
Léonie